Existing magnetic measurement techniques mostly measure one particular parameter of a magnet or magnetic system. A Gaussmeter e.g. measures the magnetic field at one position in space. A Helmholtz coil e.g. measures the integrated magnetic moment of a magnet. Recently a new magnetic measurement method and apparatus was invented, called a ‘magnetic field camera’, which is able to record high resolution 2D magnetic field maps at high speeds. This system consists of a semiconductor chip with an integrated 2D array of magnetic field sensors, which each independently measure the local magnetic field. The sensors in the array are closely spaced at very well defined relative distances, due to the well-controlled standard chip manufacturing process. The large number of pixels that independently measure the magnetic field result in a large amount of information contained within the resulting magnetic field map, which is not readily apparent and can only be extracted using advanced data analysis, such as the method described in the present invention.
On the other hand, magnetic field simulations are widely used to investigate, develop and design magnets and magnetic systems. Many magnetic field simulation software packages are commercially available. Most of them use a finite element modeling (FEM) algorithm, allowing the simulation of complex shapes and combinations of magnets and magnetic systems, as well as nonmagnetic materials. Apart from these FEM-based algorithms, analytical expressions also exist for a number of highly symmetric and simple geometrical magnet shapes, such as blocks, spheres, spheroids and ellipsoids. Analytical models can calculate faster than FEM models, but are restricted in the type of magnetic systems they can simulate. For example, they can only simulate magnets with uniform magnetization. Also they cannot simulate systems involving relative permeabilities other than unity.
Analytical models exist e.g. for uniformly magnetized spheres, block magnets (see R. Engel-Herbert and T. Hesjedal, ‘Calculation of the magnetic stray field of a uniaxial magnetic domain’, JOURNAL OF APPLIED PHYSICS 97, 074504, 2005) and spheroids (see M. Tejedor, H. Rubio, L. Elbaile, and R. Iglesias, ‘External Fields Created by Uniformly Magnetized Ellipsoids and Spheroids’, IEEE TRANSACTIONS ON MAGNETICS. VOL. 31, NO. I., JANUARY 1995). Other geometries, such as cylinders, rings, segments etc. can be built by building them up from a number of these elementary geometries. Any geometry can e.g. be approximated by a sufficiently large collection of blocks. Since the magnetic fields of a collection of magnets are additive, the magnetic field distributions of all blocks can simply be added together in order to obtain the complete magnetic field distribution.